Which way does the lower arm of a two-joint Technic-style linkage point?

The lower arm’s direction is the upper arm’s direction plus the turn at their connecting hinge. Those angles need a shared sign convention. With the upper arm fifteen degrees right of down and the lower hinge fifteen degrees back to the left, the lower arm faces down again. Its position still changes because the upper arm carries its hinge sideways.

Build two real hinges

The new Two-Joint Angle Bench makes that reference change visible. Two braced posts carry a retained main axle. A yellow five-hole arm hangs freely from one round hole. Its far end carries another retained axle and a shorter red three-hole arm. The arms occupy separate parallel planes, with bushes seated against the actual bearing faces. The second hinge travels with the yellow arm.

This is a serial chain: one link follows another. It is a different question from the Pivot Position Bench, whose arms hang independently from a common fixed support. It also differs from the closed Parallel Motion Bench, where a second connection constrains a bar’s heading. Adding a hinge does not automatically create a parallelogram or make the end stay level.

Shafie Shahrin’s credited independent double-pendulum demonstration inspired the question about one moving pivot carrying another. Our compact stock-parts layout, retained shafts, limited angles and assembly sequence are original. We do not recreate that display or claim its motion for our model. The inspected demonstration and brief project description do not provide the complete inventory and assembly sequence used here.

Predict before changing the angles

Imagine holding the yellow arm fifteen degrees to the right of vertical. If the red arm lies along the same downward direction as the yellow arm, its hinge angle relative to yellow is zero. It is still fifteen degrees from the room’s vertical. Now turn the red arm fifteen degrees back relative to yellow. Predict its direction before changing the controls.

The lab calls rightward lean positive. Upper direction is measured from down; lower hinge turn is measured from the upper arm’s downward continuation. The red arm’s direction from down is their sum. Opposite signed angles can cancel direction without cancelling position. At plus fifteen and minus fifteen degrees, the tip is about eight point two eight millimetres to the side of the fixed pivot’s vertical reference. That calculated offset comes from the upper arm moving its lower hinge.

The yellow pivot spacing is four hole gaps, or thirty-two millimetres. The red pivot-to-tip spacing is two gaps, or sixteen millimetres. These are pin-centre dimensions, not the plastic’s outside lengths. The diagram projects both arms onto the front plane; their real depth separation is omitted. It predicts positions for ideal rigid links, without fitting a measured physical prototype.

Make a fair reference-angle experiment

Complete the free instructions and inspect every retainer before moving the arms. Put the frame on a level surface and hold only that stationary frame. Place a vertical reference beside the model, clear of all moving parts. View from the front; changing camera angle between observations introduces perspective differences that can look like a mechanical error.

Gently set both arms near down. Change one angle at a time, staying within fifteen degrees at each hinge. These are manual configurations, not release-and-timing trials. The model has no physical angle stops. Do not force it through a full rotation or add a motor. Stop for rubbing, loose bushes or support movement, and repair the assembly before continuing.

Repeat each setting three times. Keep the beams, chosen holes, viewing direction and reference line unchanged. Record play, difficulty setting an angle and uncertainty rather than copying the lab values into an observation column. We have not physically tested this bench, measured its accuracy or established a payload rating. A real beam’s flex and bearing clearance can change what you see.

A repeating movie is not a chaos experiment

Double-pendulum demonstrations often prompt questions about whether complex motion is random or whether a looping clip proves a repeating physical path. First separate geometry from dynamics. Geometry describes positions once angles are specified. Dynamics must determine how those angles change from forces, masses, initial conditions and friction. Our controls specify the angles; they do not solve that second problem.

The native animation uses deliberately chosen gentle hinge motions to show a moving pivot. Its repetition is a display choice. It is not evidence of chaotic behavior, natural period, energy conservation or a successful physical release test. That limit makes the lesson useful: you can learn to name an angle correctly before tackling a full dynamical model.

Repair the constraint before explaining the motion

If the red beam slides along its shaft, inspect both neighbouring bushes. If the complete shaft moves with its bushes, inspect the stops around the yellow bearing too. If the long upper axle shifts through both posts, check its outer caps. The axle guide and bush guide explain the difference between a rotational bearing and axial retention.

Do not squeeze a joint tight to hide play, or hold a moving arm in place to replace missing support. Check the two fixing points on each post. Then return to the linkage idea page and explain which angle is measured from which reference. Predict, set one variable, observe and explain the difference between direction and position.